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The equation of line m is 3x−5y=−4.

What is the slope of a line that is perpendicular to line m?



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maxhwoy
First, write your equation in slope-intercept form, or form y = mx + b:
1) Solve for 5y:
3x - 5y = -4
3x + 4 = 5y
2) Divide everything by 5:
y = 3x/5 + 4/5
Now, we got it.
In this line slope is 3/5 because it is multiplier for x, and, the rule is that
m * p = -1
where m is the slope of the line, and p is the slope of the line perpendicular to this.
3) Now, solve there for p by plugging in value for m:
p = -1/m
p = -1 / (3/5) = -5/3
4) Now just write the equation in this form: y = px + b:
y = -5x/3 + b
This is the equation of the line perpendicular to the given one. Hope this helps!

The slope of the line that is perpendicular to the line m with equation 3x−5y=−4 is -5/3

The given equation is:

3x - 5y   =  -4

Express the equation in the form y = mx  +  c

[tex]3x - 5y = -4\\5y = 3x + 4\\y = \frac{3}{5}x + \frac{4}{5}[/tex]

Comparing [tex]y = \frac{3}{5}x + \frac{4}{5}[/tex] with y = mx + c

The slope, m = 3/5

The slope perpendicular to to the line m will have a slope that is the negative inverse of m.

That is

[tex]m_2 = \frac{-1}{\frac{3}{5} } \\\\m_2 = -1 \times \frac{5}{3}\\\\m_2 = \frac{-5}{3} \\\\[/tex]

The slope of the line that is perpendicular to the line m with equation 3x−5y=−4 is -5/3

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